Post #35 New Resources to Aid in Standards-Based Instruction
KYAE Skills U has recently posted two new resources to aid instructors in organizing and teaching the CCR Standards for Mathematics.
- Instructors will appreciate this math course outline, complete with cited materials. It was developed by instructors in programs who participated in the CCR Standards-in-Action initiative. The outline can be found on the left side of the KYAE Skills U standards-based instruction page. Click here to access.
- This helpful resource from OCTAE will assist instructors in determining how to organize their instructional time to concentrate on areas of focus for Levels D and E content, Guide to Effectively Managing Higher-Level Content Standards in Mathematics.
On a personal note, I want to inform Math Matters readers that this will be my final post, as I am retiring from KYAE Skills U August 1st. I am pleased that the torch is being passed to our newly-hired mathematics specialist and Director of the Morehead State Adult Education Academy, Pam Callahan. I look forward to following Math Matters as a reader.
Post #34 How Teacher Prep Programs Can Help Teachers Teach Math Conceptually
Many math instructors teach math concepts the same way they were taught – by using gimmicks to memorize rules and procedures, applying rules and formulas without understanding “why” they work, and not really caring why as long as the result was a correct answer. These methods may work well when simple computation is the goal; however, when students are asked to apply their isolated procedural understanding to solve real-world situational problems, they are often frustrated.
“Teaching for conceptual understanding” is all about the “why” along with the “how.” The rigor of the College and Career Readiness Standards for Mathematics (CCRSM) requires that conceptual understanding be balanced with procedural skill and real-world application. But what does “teaching for conceptual understanding” actually look like?
The conclusions of a study published in the Harvard Educational Review identifies four observed hallmarks of teaching for conceptual understanding. The article is posted on the Teaching Now blog from Education Week Teacher.
“The researchers identified four hallmarks of what it means to teach mathematics conceptually:
- Using mathematical language. Teachers should use academic language purposefully. That practice helps students develop a technical understanding of the meaning of the words. A past study found that children who were exposed to explicit number names in pre-kindergarten showed a consistently stronger performance in math than their peers for up to six years later.
- Using visual representations. These representations help students make sense of mathematical concepts and understand mathematical structures and the relationships between quantities. Ideally, researchers say students should be able to flexibly use different representations for the same mathematical concepts.
Pressing students for explanations. Doing so allows students to further develop their understanding by working through obstacles and contradictions and reaching for connections across strategies.
- Teachers should establish classroom norms, researchers say, where a good explanation is a mathematical argument and not simply a description of the procedures, and errors are further opportunities to learn.
- Using story problems. Problems with illustrative contexts connected to the real world can help develop students’ understanding. When done in a way that challenges students’ thinking, the story problems give students a familiar metaphor, they are interesting, and they enhance transfer of learning.”
Post #33 Challenging the Status Quo in Mathematics: Teaching for Understanding
Best explanation I’ve seen yet on teaching for understanding! Not only does this commentary by Christopher Rakes look at the big picture, it presents examples of what teaching for understanding looks like for certain math concepts. It just makes so much sense! Please take a moment to read it.
Post #32 What I Learned by Recording My Classes
In this blog post by Michelle Russell, read about how beneficial it can be to record your class and then reflect on what you see. Michelle shares information on the affordable tools she used and the ways this practice has changed her as a teacher.
Post #31 Power in Numbers, Advancing Math for Adult Learners
Jo Boaler is partnering with OCTAE on a new project to improve adult learning of mathematics. It is called Power in Numbers, Advancing Math for Adult Learners. OCTAE is seeking “20 teachers who are currently teaching secondary math to adult learners to identify, evaluate, and review 4-6 math OER in their classroom over 8-10 weeks.” If you are interested in helping, you can sign up on their website here. The application deadline is June 30, 2017.
Post #30 Graphing and Writing: When ELA and Math Collide
A great way to connect writing and mathematics is to have students draw graphs depicting events in a word problem. This recent blog post by Meghan Everette, Graphing and Writing: When ELA and Math Collide explains how graphing can boost understanding of word problems for students. She also includes samples and links to other resources for steps to solving word problems.
Post #29 How to Help Ensure Tech Supports Math Learning
In this blog post, Kathy Liu Sun, assistant professor of education and former high-school math teacher, shares tips for choosing technology to support math instruction. I found the post through the Math Education SmartBrief distribution mailing I receive daily, email@example.com. If you’re interested in what is happening around the nation in math education, I highly recommend subscribing to this list. Each day, you receive links to, and a short description of, articles/posts in the areas of math teaching and learning, curriculum, STEM, and policy and legislation. It only takes a moment to scan the titles for something that peaks your interest.